Content uploaded by Steve Keen
Author content
All content in this area was uploaded by Steve Keen
Content may be subject to copyright.
Keynes’s ‘revolving fund of finance’ and transactions
in the Circuit
By Steve Keen
1
Keynes’s primary motivation in writing “Alternative theories of the rate of Interest”
and “The “ex-ante” theory of the rate of interest” was to counter attempts by Ohlin and
others to recast his liquidity preference theory as no more than a supply and demand
model of the determination of the rate of interest. This rearguard action was ultimately
unsuccessful, given the profession’s ultimate acceptance of Hicks’s IS-LM analysis as a
summary of the General Theory. However, it also had a positive outcome, as tussling
with Ohlin’s arguments led Keynes to propose that investment finance was “an additional
demand for money” (Keynes 1937b: 247) to the General Theory’s triumvirate of
transactions, precautionary and speculative demands.
Keynes’s musings on the interplay between firms who wish to borrow to finance
investment, and banks that provide that finance, is prescient of, and of course partly
inspired, the Circuitist School’s later contribution. But Keynes’s less formal logic also
reached some conclusions contrary to current Circuitist belief. Keynes was correct on
these points, while recent Circuitist literature is in error. Notwithstanding this however,
the contributions of Graziani et alia on the nature of a monetary economy are essential to
the development of a proper model of Keynes’s “revolving fund of liquid finance”
(Keynes 1937c: 666).
THE REVOLVING FUND
Keynes identifies three sources of confusion between himself and Ohlin, Hicks and
Robertson (Keynes 1937b: 241-246); the third of these—a confusion between the money
needed to initiate an investment, and the money needed while investment is actually
proceeding—led to the development of the concept of a finance demand for money:
I proceed to the third possible source of confusion, due to the fact
(which may deserve more emphasis than I have given it previously) that
an investment decision (Prof. Ohlin’s investment ex-ante) may
sometimes involve a temporary demand for money before it is carried
out, quite distinct from the demand for active balances which will arise
as a result of the investment activity whilst it is going on. (Keynes
1937b: 246)
Keynes emphasizes that, if a planned investment is to be turned into an actual one,
then the investor will have a need for money that precedes the investment itself:
Planned investment—i.e. investment ex-ante—may have to secure its
“financial provision” before the investment takes place; that is to say,
before the corresponding saving has taken place… There has, therefore,
to be a technique to bridge this gap between the time when the decision
1
Associate Professor of Economics & Finance, University of Western Sydney, Australia;
www.debunkingeconomics.com
to invest is taken and the time when the correlative investment and
saving actually occur. (Keynes 1937b: 246)
This finance could be secured either by new equity or new bank debt. In either case,
there will be an imbalance between the market’s commitments to finance these ventures,
and actual savings at that point in time, which generates a “finance demand for money”.
Keynes argues that this should be considered a fourth, additional motive for desiring
money in addition to the transactions, precautionary and speculative motives detailed in
the General Theory:
Investment finance in this sense is, of course, only a special case of the finance
required by any productive process; but since it is subject to special fluctuations of its
own, I should (I now think) have done well to have emphasised it when I analysed the
various sources of the demand for money. (Keynes 1937b: 247)
Keynes’s discussion of how this demand might be met strengthens Dow’s case, that
Keynes viewed the money supply as endogenous (Dow 1995). Though he observes that
additional finance demand for money might drive up the rate of interest—which is
consonant with a fixed, exogenously determined money stock—he also countenances that
the banking system might meet this demand with an additional supply—which implies an
endogenous process of money creation:
Now, a pressure to secure more finance than usual may easily affect the rate of interest
through its influence on the demand for money; and unless the banking system is
prepared to augment the supply of money, lack of finance may prove an important
obstacle to more than a certain amount of investment decisions being on the tapis at the
same time. (Keynes 1937b: 247; emphasis added)
Keynes continues that the decision to supply money as finance for investment is an
important determinant of the level of economic activity. Thus while he rejected the
“classical” view that savings determined investment, he argued that finance determines
investment, and investment in turn determines savings.
It is the supply of available finance which, in practice, holds up from
time to time the onrush of ‘new issues.’ But if the banking system
chooses to make the finance available and the investment projected by
the new issues actually takes place, the appropriate level of incomes
will be generated out of which there will necessarily remain over an
amount of saving exactly sufficient to take care of the new investment.
(Keynes 1937: 248)
In making this case, Keynes also states unambiguously that banks control the supply
of money:
The control of finance is, indeed, a potent, though sometimes
dangerous, method for regulating the rate of investment (though much
more potent when used as a curb than as a stimulus). Yet this is only
another way of expressing the power of the banks through their control
over the supply of money—i.e. of liquidity. (Keynes 1937: 248)
Money is thus an endogenous variable, with its determination involving both the
desire by firms to invest, and the willingness of banks to lend. Keynes starts his
consideration of this process with a constant level of investment—i.e., with a steady
stream of investment projects coming forward over time, so that the rate of change of
aggregate investment with respect to time is zero. In this case, Keynes argues that a
constant stream of investment can be financed by a fixed pool of money, which turns
over continuously:
If investment is proceeding at a steady rate, the finance (or the
commitments to finance) required can be supplied from a revolving
fund of a more or less constant amount, one entrepreneur having his
finance replenished for the purpose of a projected investment as another
exhausts his on paying for his completed investment. (Keynes 1937b:
247)
This implies that a constant level of economic activity can be sustained by a constant
stock of money—since investment in turn determines the level of income, and a constant
level of gross investment implies a constant capital stock. Rising investment, on the other
hand, implies rising capital and rising output, and here Keynes argues that there will be a
rising demand for money for finance: “if decisions to invest are (e.g.) increasing, the
extra finance involved will constitute an additional demand for money” (Keynes 1937b:
247).
As noted above, Keynes countenances that this demand could put upwards pressure on
the rate of interest, if banks did not generate more money. But it could also lead to banks
increasing the money supply “if the banking system chooses to make the finance
available”. In tranquil times, banks would willingly supply additional finance when firms
desired a rising level of investment, and this in turn would cause rising incomes over
time. The demand for money would thus call forth its supply.
Keynes concludes with observations about the tendency of economists to confuse
finance and saving, and stocks and flows. “‘Finance’”, he emphatically declared,
has nothing to do with saving. At the ‘financial’ stage of the
proceedings no net saving has taken place on anyone’s part, just as
there has been no net investment. ‘Finance’ and ‘commitments to
finance’ are mere credit and debit book entries, which allow
entrepreneurs to go ahead with assurance. (Keynes 1937b: 247).
Keynes’s conjecture that confusion between stocks and flows was the source of
important errors in monetary theory is worth quoting at length:
It is possible, then, that confusion has arisen between credit in the sense
of ‘finance,’ credit in the sense of ‘bank loans’ and credit in the sense of
‘saving.’ I have not attempted to deal here with the second. It should be
observed that a confusion between the first and the last would be one
between a flow and a stock. Credit, in the sense of ‘finance,’ looks after
a flow of investment. It is a revolving fund which can be used over and
over again. It does not absorb or exhaust any resources. The same
‘finance’ can tackle one investment after another. But credit, in Prof.
Ohlin’s sense of ‘saving,’ relates to a stock. Each new net investment
has new net saving attached to it. The saving can be used once only. It
relates to the net addition to the stock of actual assets. (Keynes 1937b:
247; emphasis added)
Keynes’s concept of a finance demand for money thus provides a link between a flow
of demand for credit money, and the stock of credit money that is needed to meet that
flow demand, given the time lags in the economy.
Unlike Keynes, the Circuitist School has attempted to deal with “credit in the sense of
‘bank loans’”. In so doing, they have reached several conclusions that implicitly or
explicitly contradict Keynes.
Keynes implicitly argues that capitalists could make aggregate money profits, after
borrowing money at positive rates of interest, when he speaks of “one entrepreneur
having his finance replenished for the purpose of a projected investment as another
exhausts his on paying for his completed investment”. In contrast, Circuitists explicitly
allege that capitalists cannot make aggregate monetary profits, even if the rate of interest
is zero:
“in the basic circuit approach (describing a closed economy with no government
expenditure), firms in the aggregate can only obtain the wage bill they advanced to
workers (w
N
) and, as a result, it is impossible for all firms to obtain money profits.”
(Bellofiore et al. 2000: 410)
1
Keynes argues that constant economic activity could be supported with a constant
stock of money, regardless of how workers allocated their wages. Circuitists claim that a
constant level of activity requires an increasing stock of money if workers save, since
with part of the borrowed money saved, firms are unable to repay their bank loans in full:
If, as is likely to be the case, firms wish to continue their activities, they
have to renegotiate bank loans equal to the net stock of money in
addition to any lending necessary to start a new production process.
(Fontana 2000: 35)
Crucially, Keynes sees money turning over indefinitely in “revolving fund of liquid
finance”—so that money, once created, exists forever (though he did not consider the
issue of bankruptcy). On the other hand, in Circuitist literature, money is “destroyed”
when loans are repaid:
“To the extend that bank debts are repaid, an equal amount of money is
destroyed” (Graziani 2003: 29-30)
In all these points of contradiction, Keynes is correct and the Circuitists are wrong, for
the reason Keynes gave in 1937: Circuitists, like so many economists before them, have
confused stocks with flows. However, Circuitist insights into the nature of money, and of
exchange in a monetary economy, play a crucial role in turning Keynes’s accurate verbal
insights into a workable mathematical model of a monetary production economy.
THE CANONICAL CIRCUITIST INSIGHTS
The three key contributions of the Circuitist School are:
• The proposition that a true monetary economy cannot use a commodity as
money;
• The insight that exchanges in a monetary production economy are three-sided,
single commodity transactions; and
• A logical definition of money that is free of the customary confusions that arise
from defining money in terms of different types of bank deposits.
The first proposition is derived from the simple observation that “an economy using as
money a commodity coming out of a regular process of production, cannot be
distinguished from a barter economy” (Graziani 1989: 3). From this it follows that true
money is a token, which in turn gives rise to two further conditions, that:
the use of money must give rise to an immediate and final payment and
not to a simple commitment to make a payment in the future; and
the use of money must be so regulated as to give no privilege of
seigniorage to any agent. (Graziani 2003: 60)
These conditions lead to the second fundamental insight, that all sales in a monetary
economy involve three parties: a seller, a buyer, and a bank which transfers the requisite
number of units of account from the buyer’s account to the seller’s.
These in turn provide a definition of money that enables it to be clearly distringuished
from credit—another confusion that Keynes notes. Money is as a unit of account whose
transfer is accepted as final payment in all commodity and service exchanges; credit, on
the other hand, enables a commodity or service exchange to occur, but involves a
continuing debtor-creditor relationship between the buyer and the seller.
CIRCUITISTS AND CHARTALISTS
The State plays no necessary role in the above definition of money—though
Circuitists of course acknowledge the existence of “fiat” money, and generally accept the
Chartalist or state theory of money position with respect to the origins of money and its
modern legal framework (see for example Graziani 2003: 78-80). However, this School
has attempted to build models which at the outset have no government sector—nor any
explicit role for the Central Bank (Graziani 2003: 26-32). In this sense, the Circuit
approach conflicts with the Chartalist argument that “It is thus impossible to separate the
theory of money from the theory of the state” (Wray 2000: 50).
From the Circuitist point of view, the production and enforcement of a unit of
account by a tax-levying state is an embellishment to its fundamental concept of money.
The Circuitist starting point of a pure credit economy is thus arguably closer to the
essential nature of money, even if so-called “State Money” is the universal norm today,
and even State enforcement of monetary obligations may be the only viable way to
sustainably meet Graziani’s anti-seignorage condition in the real world.
However, the failure to date of Circuitists to produce a coherent model of endogenous
money could have implied that the Chartalist position was correct, in that a tax-levying
state was indeed an essential component of a functional model of money. In fact, as I
show below, a functional model of a monetary production economy can be built without
either a government sector or a central bank, so long as transfers between private bank
accounts are accepted as making final settlement of debts between buyers and sellers.
THE BASIC CIRCUITIST MODEL
Graziani 2003 presents a canonical version of the Circuitist verbal model of a
monetary production economy. The model is described as having four classes of agents—
“the central bank, commercial banks, firms and wage earners” (26-27) —but despite this,
the central bank is given no role in the model itself. The actual model therefore has only
three agents.
2
The model’s monetary dynamics commence with “A decision ... by the banks to grant
credit to firms, thus enabling them to start a process of production” (27). Graziani argues
that the amount of credit demanded by the firms (and supplied by the banks) equals the
wage bill for the planned level of production.
Using the borrowed money, capitalists pay workers and put them to work to produce
commodities. These are then sold, with consumer goods being sold to workers and
investment goods to other capitalists (sales to bankers appear later).
Spending by workers on consumer goods (and also purchases of corporate bonds by
workers) return money to the firms, who can then use this money to repay their debt to
banks. This repayment of debt destroys money: “To the extend that bank debts are repaid,
an equal amount of money is destroyed” (29-30).
The repayment of debt closes the circuit, but this only happens “If wage earners spend
their incomes entirely” (including on purchases of corporate bonds). However if they
don’t, then dilemmas arise:
If instead wage earners decide to keep a portion of their savings in the
firm of liquid balances, firms are unable to repay their bank debt by the
same amount. (30)
The next cycle, if it involves an identical scale of production, therefore requires new
money, so that the money supply must increase to finance a constant scale of production.
The new quantity of money in this second circuit “will be equal to the wage bill plus the
new liquid balances set aside by wage earners at the end of the previous cycle” (31).
The above, however, omits the problem of interest on debt! Graziani acknowledges
this—in contrast to some Circuitist papers that abstract from the problem, in a manner
that is embarrassingly reminiscent of the neoclassical approach to logical conumdrums
(Bellofiore et al. 2000: 410—footnotes 8 and 9). It appears that firms are unable to pay
interest:
even in the most favourable case [corresponding to workers spending
all their wages], the firms can only repay in money the principal of their
debt and are anyhow unable to pay interest. (31)
The solution he proffers, in a monetary model, is a “real” one, that banks are paid in
commodities rather than money: “the only thing they can do is to sell part of their product
to the banks, which is tantamount to saying that interest can only be paid in kind” (31).
At least bankers get their hands on the physical loot: capitalists, it seems, end up with
neither goods nor money. Money profits in the aggregate are zero, and “profits earned by
one firm may simply be the mirror image of inefficiencies and consequent losses incurred
by other firms” (32).
A DYNAMIC MODEL OF THE CIRCUIT
Starting from precisely the same foundation, I reach contrary conclusions on almost
every point above, and conclude instead that Keynes’s 1937 insights were correct. A
constant level of production can be financed with a constant stock of money (see also
Andresen 2006); firms can easily pay the interest on debt with money; and firms in the
aggregate earn money profits. Money is not destroyed by the repayment of debt (though
bank deposits are “destroyed” by loan repayment, and the stock of money available for
transactions at any one time is reduced); workers can have positive bank balances without
forcing firms to make losses; and, though it is related to the wage bill, the initial amount
borrowed is in fact far smaller.
These contrary conclusions arise simply from applying the correct form of
mathematical analysis to the Circuitist school’s logical insights into the nature of a
monetary production economy. The Circuit is fundamentally dynamic, and can therefore
only be properly understood using dynamic analysis. Mathematical dynamics are
essential here, partly because the interrelations between entities in a dynamic model are
easily mis-specified in verbal analysis, and especially because it is easy, in a verbal
exposition, to confuse stocks and flows. In what follows, I construct a skeletal dynamic
mathematical model of the Circuit, using balance sheets in which all entries are flows.
The model is, I stress, deliberately skeletal: causal factors of financial flows that are
clearly variables in the real world are treated as constants—with the intention that these
will indeed be made variables in a later model. However, just as much is learnt in
anatomy by studying skeletons, much can be learnt about the actual monetary systems by
studying a stylized system in which the causes of financial instability are absent.
Graziani’s model has three classes of agents—firms, bankers, and workers. Since this
is a monetary economy, all three classes have deposit accounts which I indicate as F
D
, B
D
and W
D
respectively. Prior to the making of a loan, all three accounts have zero balances,
and firms’ debt to banks F
L
is likewise zero (this is not a bank account as such: it does
not contain money, nor can money be paid into it, but it instead records the outstanding
obligation of the firms to the banks; it is, therefore, a record of account). This “ab initio”
situation is shown in Table 1.
Bank Assets & Liabilities
Assets Liabilities Time
Firm Loan
(F
L
)
Firm Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker Deposit
(W
D
)
Initial
values
0 0 0 0
Table 1: Initial conditions prior to loan
In step one of the model, banks make loans to the firms. Since this is credit money, a
debt obligation is created between the firms and banks along with the creation of money.
Using L to signify the magnitude of the loan, this results in the situation shown in Table
2. This clearly embodies the direct and causal “loans create deposits” perspective of
endogenous money.
Bank Assets & Liabilities
Assets Liabilities Time
Firm Loan
(F
L
)
Firm Deposit
(F
D
)
Banker Deposit
(B
D
)
Worker Deposit
(W
D
)
Start of
loan
L L 0 0
Table 2: Loan issued
A loan generates an obligation to pay interest to the lender, while a deposit obligates
the bank to pay interest to the depositor. I use r
L
for the rate of interest on loans and r
D
for
the rate on deposits, (where r
L
>r
D
). These obligations are shown in Table 3.
Bank Assets & Liabilities
Assets Liabilities Time
Firm Loan
(F
L
)
Firm Deposit
(F
D
)
Banker Deposit
(B
D
)
Worker Deposit
(W
D
)
Obligations
initiated by
loan
+r
L
F
L
+r
D
F
D
0 0
Table 3: Loan and deposit obligations
We now move from the loan obligations to the flows which must occur out of
accounts in the system—since there is no other source of money. The firms must
therefore pay the loan interest obligation out of their deposit account F
D
, while the bank
must pay its deposit interest obligation out of its deposit account B
D
.
The flows occur between these two deposit accounts, and the payment of loan interest
is recorded on the asset side of the ledger, so that the firms’ debt remains constant at the
level of the initial loan L. Since the interest payments flow between the firm and banker
deposit accounts, the overall sum of deposit accounts also stabilises at L; but since r
L
>r
D
,
the balance shifts from the firms deposit account to the bankers over time. This dynamic
is shown in Table 4.
Bank Assets & Liabilities
Assets Liabilities SAM Flows
Firm
Loan
(F
L
)
Firm
Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker
Deposit
(W
D
)
Sum
Interest
flows
initiated
by loan
+r
L
F
L
-
r
L
F
L
=0
+r
D
F
D
-
r
L
F
L
+r
L
F
L
- r
D
F
D
0 0
Table 4: Payment of interest
Equation (0.1) states this incomplete system as a set of coupled ODEs. It is obvious
that the level of debt will remain constant (at the initial value L), as will the sum of
deposit accounts, but the money in the firms’ account will over time be transferred to the
banks’. At some point, firms’ deposit accounts will turn negative—which is of course an
unsustainable situation.
=
= −
= −
=
0
0
d
L
dt
d
D D D L L
dt
d
D L L D D
dt
d
D
dt
F
F r F r F
B r F r F
W
(0.1)
Figure 1 shows a simulation of this system. Given the set of example parameter values
(L=100, r
L
=5%, r
D
=3%) while the outstanding loan and the sum of deposit accounts
remain at 100 throughout, all the money has been transferred from the firms’ deposit
account to the bankers’ after 30.5 years.
Given
Initial values Flow dynamics
Firm loan account
F
L
0( ) L=
t
F
L
t( )
d
d
r
L
F
L
t( )⋅ r
L
F
L
t( )⋅−=
Firm deposit account
F
D
0( ) L=
t
F
D
t( )
d
d
r
D
F
D
t( )⋅ r
L
F
L
t( )⋅−=
Bank deposit account
B
D
0( ) 0=
t
B
D
t( )
d
d
r
L
F
L
t( )⋅ r
D
F
D
t( )⋅−=
Worker deposit account
W
D
0( ) 0=
t
W
D
t( )
d
d
0=
F
L
F
D
B
D
W
D
Odesolve
F
L
F
D
B
D
W
D
t, Y,
:=
0 5 10 15 20 25 30
0
50
100
0
50
100
Firm Loan
Firm Deposit
Bank Deposit (RHS)
Worker Deposit (RHS)
Circuit Model Step One: Interest payment only
Time
Account Balances
F
D
Y( ) 0= B
D
Y( ) 100= W
D
Y( ) 0= F
D
Y( ) B
D
Y( )+ W
D
Y( )+ 100=
Figure 1: Simulation of interest payment only model in Mathcad
This outcome possibly explains why Circuitists have been loathe to acknowledge the
need to pay interest in their models of the monetary circuit: the situation seems hopeless
for firms. However, this is only because firms have not yet done anything with the
borrowed money. In fact, it has been borrowed to finance production, which involves
both buying inputs from other firms, and paying wages to workers. This in turn is done in
order to evoke a stream of purchases from other firms, workers and bankers from which
the firms hope to make a net profit.
The issue of production, and the transactions enabling it and emanating from it, is
another area of great confusion in Circuitist writings. The key confusion is one of stocks
and flows, starting from the proposition that the size of the initial loan (the stock L) is
equal to the wage payments needed to hire the workforce (a flow). Instead, the wage bill
is related, not to the initial loan, but to the rate of outflow of money from firms’ deposit
accounts that is used to pay wages. Calling this rate of outflow w, an amount w.F
D
is
transferred per unit of time (per year in this model) from firms to workers as wages.
Bank Assets & Liabilities
Assets Liabilities SAM
Flows
Firm Loan
(F
L
)
Firm
Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker
Deposit
(W
D
)
Sum
Wage flow to initiate
production
-w. F
D
+w. F
D
0
Table 5: Spending to finance production
The relationship between money and wages is thus not “the credit initially granted [L,
a stock] is totally turned into wages [w.F
D
, a flow]” (Graziani 2003: 29). Instead, in this
skeletal model, wages equal a constant times the balance in the firms’ deposit account.
3
Given the relationship between the initial loan and the balance in the firms’ account, the
annual wages paid can be substantially greater than the initial loan.
With workers now having positive bank balances, they too are receipients of interest
income. Though in the real world workers normally get lower deposit rates than firms, for
simplicity I will use the same rate of interest r
D
here. A flow of r
D
.W
D
is therefore
deducted from the bankers’ account and deposited into the workers’ account.
Bank Assets & Liabilities
Assets Liabilities SAM
Flows
Firm Loan
(F
L
)
Firm
Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker
Deposit
(W
D
)
Sum
Interest income
flows from wages
- r
D
. W
D
+r
D
. W
D
0
Table 6: Incomes from production
To complete the model, we have to include the flow of transactions from workers and
bankers to capitalists that purchase the goods flowing (implicitly in this model) in the
opposite direction. Here I use
ω
for the rate at which spending flows from workers’
deposit accounts to firms’, and
β
for the corresponding rate of spending by banks. The
amounts
D
W
ω
⋅
and
D
B
β
⋅
are therefore deducted from workers and banks accounts
respectively and credited to the firms’ account.
The basic model is finally complete, and as shown by the sum column of the Social
Accounting Matrix, all transactions are properly accounted for and sum to zero—so that
money is neither created nor destroyed. The components of the basic coupled ODE model
can now be read down the columns of the final 4 rows of Table 7.
Bank Assets & Liabilities
Assets Liabilities SAM Flows
Firm
Loan (F
L
)
Firm
Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker
Deposit
(W
D
)
Sum
Interest
flows
initiated by
loan
0
+r
D
.F
D
-
r
L
.F
L
+r
L
.F
L
- r
D
.F
D
0 0
Wage flow
to initiate
production
-w. F
D
+w. F
D
0
Interest
income
flows from
wages
- r
D
. W
D
+r
D
. W
D
0
Flows from
sale
D
D
W
B
ω
β
+ ⋅
+ ⋅
D
B
β
− ⋅
D
W
ω
− ⋅
0
Table 7: Transactions complete the basic model
In coupled ODE form, the model is as shown in Equation (0.2).
( ) ( )
( )
ω β
β
ω
=
= − − ⋅ + ⋅ + ⋅
= − − ⋅ − ⋅
= ⋅ + ⋅ − ⋅
0
d
L
dt
d
D D D L L D D D
dt
d
D L L D D D D D
dt
d
D D D D D
dt
F
F r F r F w F W B
B r F r F r W B
W w F r W W
(0.2)
The model can now be simulated (see Figure 2; the additional parameter values used
here are w=3,
26
ω
=
and
0.5
β
=
), and since it is a linear model, its equilibrium can
also be derived symbolically (see equation (0.3))
0 5 10 15 20 25 30
85
90
95
100
0
5
10
15
Firm Loan
Firm Deposit
Bank Deposit (RHS)
Worker Deposit (RHS)
Basic Circuit Model
Time
Account Balances
F
D
Y( ) 85.83= B
D
Y( ) 4.255= W
D
Y( ) 9.915= F
D
Y( ) B
D
Y( )+ W
D
Y( )+ 100=
Figure 2: Basic Circuit model
As is now obvious, the basic Circuitist model with a single injection of endogenous
money is consistent with sustained economic activity over time—contradicting the
Circuitists since an increasing supply is not needed to sustain constant economic activity,
and confirming Keynes 1937b (see also Andresen 2006). However, the amounts shown
here are transaction account balances: we do not yet know whether these are compatible
with sustained incomes over time.
( ) ( )
( ) ( )
( )
( )
( ) ( )
ω β
ω β
β
β
ω β
⋅ − ⋅ −
+ − ⋅ −
= =
⋅ −
−
⋅ ⋅ −
+ − ⋅ −
100
85.83
4.255
9.915
E
E
E
E
D L
L
D D
D
L D
D
D
D
L
D D
L
L r r
F
w r r
F
L r r
B
r
W
L w r
w r r
(0.3)
Income dynamics
Fortunately, two income flows are easily associated with particular transactions in
equation (0.2): wages and interest income. Annual wages are equal to
D
w F
⋅
and gross
bank interest income is
L L
r F
(257.489 and 5 per annum respectively in this simulation).
Wages and interest income are thus positive and sustained; what about profits?
To reveal profits, we need to consider what the term w represents. As well as being
equivalent to wages, it also represents that part of the net surplus from production that
accrues to workers. The net surplus—in monetary terms—itself depends on how rapidly
money invested in production returns to firms. In Marx’s terms, it represents the time lag
between extending M and receiving M+ (assuming, as I do in this skeletal model, that the
process occurs smoothly). This could be a period of, say, 4 months between financing
production and receiving the complete proceeds of sale of output—again something that
would be a variable in a more complex model. There are thus two components to w: the
share of the net surplus (in Sraffa’s sense of the surplus, in which wages and profits are
entirely paid out of the net surplus from the input-output process) from production going
to workers, and the rate of turnover from M to M+, given by technical conditions of
production and the time taken for the sale of physical commodities. I use s for the share
of surplus accruing to the owners of firms (so that the share going to workers is thus 1-s),
and P for the lag between M and M+.
4
We therefore have the relation given by equation
(0.4):
(
)
= − ⋅
1
w s P
(0.4)
With w set to 3 in the simulation above, a hypothetical value of s of 0.4 (which
corresponds to a “rate of surplus value” in Marx’s terms of 67%) yields a value for P of 5
(which means that the lag between spending M and making M+ is 1/5
th
of a year or 2.4
months). The monetary value of net output per annum is thus P.F
D
(which equals 429.15
in equilibrium, given the parameter values in the model) which is split between workers
and the owners of firms in the ratio (1-s):s. In this debt-finance only model, the owners of
firms then have to pay interest on their outstanding debt to banks. Using
Π
, W and I to
signify profits, wages and interest income respectively, the income flows of the model in
equilibrium are:
(
)
(
)
( )
( )
( )
( )
( ) ( )
( )
( )
( )
ω β
ω β
ω β
ω β
⋅ − ⋅ −
⋅ ⋅
− ⋅ + − ⋅ −
Π
= ⋅ =
⋅ − ⋅ −
− ⋅ ⋅
− ⋅ + − ⋅ −
1
166.66
5
257.49
1
1
D L
D D
E
E D
E
D L
D D
L r r
s P
s P r r
I r L
W
L r r
s P
s P r r
(0.5)
Firms thus do make net profits, which, though related to the size of the initial loan, can
be substantially larger than this amount (and profits are substantially larger than the
servicing cost of debt). Economic activity also continues indefinitely at an equilibrium
level with a single injection of endogenous money: additional money is not needed to
sustain economic activity at a constant level. This contradicts Graziani’s assertion that
additional money would be needed if workers retained positive bank balances (Graziani
2003: 31), but confirms Keynes’s intuition that a “revolving fund of a more or less
constant amount” can finance sustained economic activity (Keynes 1937b: 248).
The size of the initial loan L can also be related to the equilibrium value of wages
generated by the loan:
(
)
(
)
(
)
( ) ( ) ( )
ω β
ω β
− ⋅ + − ⋅ −
= ⋅ =
− ⋅ ⋅ − ⋅ −
1
100
1
D D
E
D L
s P r r
L W
s P r r
(0.6)
Two more issues remain to be considered: the impact of debt repayment, and the
modelling of growth.
Debt repayment and bank reserves
According to Graziani—and almost all theorists in endogenous money—the
repayment of debt destroys the money that was created with it (Graziani 2003: 29-30). I
consider this by adding an additional term R
L
to represent the repayment of debt. If we
relate this to the level of outstanding debt
5
, then the amount R
L
.F
L
is deducted from the
firms’ only source of money, F
D
. Yet to where does it go?
Here Graziani’s anti-seignorage condition comes into play: “the use of money must be
so regulated as to give no privilege of seigniorage to any agent” (Graziani 2003: 60). This
repayment therefore cannot be made to the existing bankers’ deposit account B
D
, since
banks use this account to finance spending on commodities. It must therefore go to a
separate, capital account: the banks’ reserve account, which I call B
R
.
Reserves, once created by the repayment of loans, will be re-lent. This amount will be
deducted from the banks’ reserve account and deposited in the firms’ deposit account—
and a matching entry will be made in the firms loan record of account. The complete
relations are shown in Table 8.
Bank Assets & Liabilities
Assets Liabilities SAM
Flows
Firm
Loan (F
L
)
Firm
Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker
Deposit
(W
D
)
Income
Repayment
of debt
-R
L
.F
L
-R
L
.F
L
-R
L
.F
L
Relending
of reserves
+L
R
.B
R
+L
R
.B
R
+L
R
.B
R
Bank Reserves
Time Reserve Account Capital
Repayment of debt R
L
.F
L
+R
L
.F
L
Relending of reserves -L
R
.B
R
-L
R
.B
R
SAM Sum 0
Table 8: Repayment and relending
The repayment of loans therefore does not “destroy” money, but transfers it out of
income accounts—where it can be used for expenditure—to a reserve account. The
proposition that money is destroyed when loans are repaid in part reflects economic
conventions that money is the sum of active bank balances. If money is defined that way,
then it is indeed destroyed; but I feel that the dynamics of endogenous money creation are
more clearly illuminated if we define money in the fundamental Circuitist sense as a
token whose transfer settles all commitments between trading parties. That token can
then reside in active accounts (deposits) or inactive accounts (reserves). Repayment of
loans alters the balance between active and inactive accounts, and thus alters the amount
of money in circulation, but it does not destroy the token itself.
Once there, it is an unemcumbered asset of the banks which can then be re-lent—
though not spent directly on commodities or services. This adds an important additional
insight to the concept of endogenous money: not only do “loans create deposits”, but “the
repayment of loans creates reserves”.
This results in the model shown in equation (0.7):
( ) ( ) ( ) ( )
( )
( )
ω β
β
ω
= + ⋅ − ⋅
= − − − ⋅ ⋅ + ⋅ + ⋅ + ⋅ − ⋅
= − − ⋅ − ⋅
= − ⋅ ⋅ + ⋅ − ⋅
= + ⋅ − ⋅
1
1
d
L R R L L
dt
d
D D D L L D D D R R L L
dt
d
D L L D D D D D
dt
d
D D D D D
dt
d
R L L R R
dt
F L B R F
F r F r F s P F W B L B R F
B r F r F r W B
W s P F r W W
B R F L B
(0.7)
The simulation results for this model are shown in Figure 3 (with a shorter time span
to show the initial dynamics). The new parameters R
L
and L
R
were given the values of 2
and 3 respectively.
Figure 3: Model with repayment and relending
The equilibrium values are shown in Equation (0.8):
( ) ( )
( )
( )
( )
( )
( ) ( )
( )
( )
( )
ω β
ω β
β
β
ω β
⋅
⋅ − ⋅ −
⋅
− ⋅ + − ⋅ −
⋅ −
⋅= ⋅ =
−+
⋅ − ⋅ ⋅ −
⋅
− ⋅ + − ⋅ −
⋅
60
1
51.5
1
2.55
5.95
1
40
1
E
E
E
E
E
R
D L
L
R
D D
D
L D
D
R
DR L
D
L
R
R
D D
L
L L
L r r
F
L
s P r r
F
L r r
B
L
rL R
W
L s P r
L
B
s P r r
R L
(0.8)
It is obvious that money is not destroyed, but turned into reserves that are then
available for relending. However, there is a reduction in money in circulation at any one
time, equivalent to the proportion of debt that has been repaid. Given the parameters used
in this simulation, the amount of circulating money is reduced from 100 to 60 units.
It is thus not money that is “destroyed” by the repayment of debt, but deposits in
income accounts. This in turn reduces the amount available for the financing of
production, reducing all incomes—including that of banks. The equilibrium levels of
income are now:
Π
=
103
3
159.49
E
E
E
I
W
(0.9)
Growth
At this stage, the model accords with Keynes’s verbal analysis of the “revolving fund
of finance” without growth. The final problem is how to model endogenous money in a
growing economy, when “decisions to invest are (e.g.) increasing” and “the extra finance
involved will constitute an additional demand for money.” (Keynes 1937b: 248).
Accounting for growth integrates Moore’s “Horizontalism” into the Circuitist
framework (Moore 1988). As Moore argues, firms negotiate “lines of credit” with banks
that enable them to expand the available money, subject to the same sum being added to
their outstanding debt. New money is thus created by an addition of an identical sum to
the firms’ deposit and loan accounts Using F
I
(for “Firms’ Investment”) to signify the
rate, and relating this to the level of firms’ deposit accounts,
6
this introduces a new term
F
I
.F
D
into the columns for F
L
and F
D
in the final table. I have included the creation and
simultaneous transfer of this new money in the banks’ reserve account simply to indicate
that the endogenous creation of money by firms depends upon the legal right they have
negotiated with banks to expand their borrowings.
7
Bank Assets & Liabilities
Assets Liabilities SAM Flows
Firm
Loan (F
L
)
Firm
Deposit
(F
D
)
Banker
Deposit
(B
D
)
Worker
Deposit
(W
D
)
Income
Investment
by firms
+F
I
.F
D
+F
I
.F
D
+F
I
.F
D
Bank Reserves
Time Reserves Capital
Investment by firms +F
I
.F
D
-F
I
.F
D
0
SAM Sum +F
I
.F
D
Table 9: Endogenous creation of new money
There is no offsetting transfer between income and capital accounts in this case, so
that the term F
I
.F
D
causes a net increase in the money stock: it is an endogenous source of
growth. As a result, rather than having a zero sum, the complete SAM has a positive sum,
equal to the amount of new money F
I
.F
D
being created each year. The overall model, as
shown in Equation (0.10), is therefore “dissipative”—in the language of modern dynamic
analysis—rather than “conservative”, which has important implications for the feasible
behaviour of any complete model built on this skeleton.
( ) ( ) ( ) ( )
( )
( )
ω β
β
ω
= + ⋅ − ⋅ + ⋅
= − − − ⋅ ⋅ + ⋅ + ⋅ + ⋅ − ⋅ + ⋅
= − − ⋅ − ⋅
= − ⋅ ⋅ + ⋅ − ⋅
= + ⋅ − ⋅
1
1
d
L R R L L I D
dt
d
D D D L L D D D R R L L I D
dt
d
D L L D D D D D
dt
d
D D D D D
dt
d
R L L R R
dt
F L B R F F F
F r F r F s P F W B L B R F F F
B r F r F r W B
W s P F r W W
B R F L B
(0.10)
Though the amount of money and debt in this final model grow exponentially over
time, the same relations hold between debt and income deposits, while the overall money
stock includes both the sum of deposit accounts and the amount in banks’ reserves. At the
end of the simulation period (30 years), the endogenous money stock has grown from 100
to 379.13, 228.78 of which is in circulation between firm, bank and worker income
accounts, and 150.35 of which is in the banks’ reserve account.
Figure 4: Model with growth
From parameters to behaviours
Like a biological skeleton, this model is designed to have muscles attached, in that its
fixed parameters can be replaced by nonlinear behavioral relations that mimic those of
real economies. Two that deserve special mention are R
L
and F
I
,, representing
respectively the rate of relending by banks and the rate of new money creation driven by
firms.
The latter provides the “Horizontalist” aspect of this skeletal model, and in a general
model would be a nonlinear function of firms’ expectations of profits (see Keen 1995).
The former reflects the Structuralist emphasis on the active role of banks in the credit
system. In a financial crisis, this would tend towards zero, while during a period of
euphoric expectations the rate of relending would accelerate.
This illustrates another advantage of dynamic modelling over the conventional
diagrammatic and static methods that Post Keynesian and Circuitist economists have in
the past applied. Diagrammatic methods are necessarily “two dimensional”, while static
methods make it difficult, if not impossible, to examine causal relations—even when they
are correctly specified, which is rarely if ever the case. On the other hand, this properly
specified dynamic model enables the integration of the Horizontalist and Structuralist
approaches (which could be further embellished by making the spread between r
L
and r
D
a variable).
Conclusion
Keynes was correct that a “revolving fund of finance” can initiate an indefinite stream
of production, and that this fund is a necessary prelude to production itself in a monetary
economy. The Circuitist formalisation of the concept of credit money plays an essential
role in converting Keynes’s vision from a verbal to a dynamic model, but at the same
time, some prevalent Circuitist concepts must be abandoned in favour of Keynes’s
accurate insights from 1937.
Both Keynes and Circuitists gain from this model. Keynes is shown, once again, to
have correctly identified the dynamics of a monetary production economy, even though
he did lacked the assistance of mathematical logic to clarify his argument. Circuitists gain
an effective expression of their model, and lose only erroneous conclusions that shackled
their capacity to achieve their real goal, of specifying the behaviour of endogenous
money in a monetary production economy.
References
Andresen, Trond, (2006), “A critique of a Post Keynesian model of hoarding, and an
alternative model”, Journal of Economic Behavior & Organization, 60: 230–251.
Chapman, Brian and Keen, Steve, (2006). “Hic Rhodus, Hic Salta! Profit in a
Dynamic Model of the Monetary Circuit”, Storia Del Pensiero Economico: 139-156.
Bellofiore, Riccardo., Davanzati, G. F. and Realfonzo, R, (2000), “Marx inside the
Circuit: Discipline Device, Wage Bargaining and Unemployment in a Sequential
Monetary Economy”, Review of Political Economy, 12: 403-17.
Dow, Sheila (1997), “Endogenous money”, in Harcourt G.C. & Riach P.A., (eds.), A
‘Second Edition’ of the General Theory, Routledge, London.
Fontana, Guiseppe., 2000. “Post Keynesians and Circuitists on money and uncertainty:
an attempt at generality”, Journal of Post Keynesian Economics, 23: 27–48.
Fontana, Guiseppe, & Realfonzo, R., (eds.), (2005), The Monetary Theory of
Production, Palgrave, New York.
Graziani, Augusto, (1989). “The Theory of the Monetary Circuit”, Thames Papers in
Political Economy, Spring,:1-26. Reprinted in Musella, M. & Panico, C., (eds.), (1995),
The Money Supply in the Economic Process, Edward Elgar, Aldershot.
Graziani, Augusto, (2003). The Monetary Theory of Production, Cambridge
University Press, Cambridge.
Keen, Steve, (1995). “Finance and economic breakdown: modelling Minsky’s
Financial Instability Hypothesis”, Journal of Post Keynesian Economics, 17: 607-635.
Keynes, J.M., (1937a), “The general theory of employment”, Quarterly Journal of
Economics, 51: 209-223.
Keynes, J.M., (1937b), “Alternative theories of the rate of interest”, Economic
Journal, 47: pp. 241-252
Keynes, J.M., (1937c), “The “ex-ante” theory of the rate of interest”, Economic
Journal, 47: pp. 663-669.
Moore, B. (1988), Horizontalists and Verticalists: The Macroeconomics of Credit-
Money, Cambridge, Cambridge: Cambridge University Press.
Rochon, Louis-Philippe, (2005), “The existence of monetary profits within the
monetary circuit”, in Fontana & Realfonzo (2005), pp. 125-138.
1
Similar conclusions are reached in numerous other Circuitist papers from Graziani 1989 on. Rochon
puts the problem well: “The existence of monetary profits at the macroeconomic level has always been a
conundrum for theoreticians of the monetary circuit… not only are firms unable to create profits, they also
cannot raise sufficient funds to cover the payment of interest. In other words, how can M become M`?”
(Rochon 2005: 125).
2
The Central Bank properly enters the Circuitist model when the banking sector is expanded, so that a
seller can deposit the proceeds of a sale in a different bank to that of the buyer. This necessitates a clearing
house between banks, which is the primary role of a Central Bank in the Circuitist model. In this paper, for
the sake of simplicity, I omit inter-bank dynamics.
3
Later I apply Graziani’s position that “the demand for bank credit coming from producers depends
only on the wage rate and on the number of workers that firms intend to hire” (29) to calculate the size of
the initial loan L as a function of the equilibrium wage bill
4
Again, in a more complete model, each of these stages of the process would have their own equation
with its own dynamics; here, for reasons of simplicity and exposition, they are all collapsed into the values
of s and P.
5
It could equally be related to the level of F
D
.
6
It could as easily be related to the level of outstanding loans, and would doubtless have a more
complex causal link in a full dynamic model.
7
In a full model, this could be given a rationing ceiling; however I believe that a better way to indicate
banks’ “structuralist” control over lending is to replace R
L
with a variable dependent upon financial
conditions.
